The aperture limits the length of the rudder stock, like most keel hung rudders. Even if you had a new rudder stock built to go around the perimeter of the aperture(some were done that way), it wouldn't be effective down low as the diameter would twist in that length under a lot of stress.

That makes a composite rudder(like the one I posted) hard to do, it takes a large rudder stock to resist the twist(the stock and skeleton are most of the structure). In fact that composite rudder design, may be simpler than what you're dealing with, because it had no aperture to deal with.

Your rudder design, similar to mine, took it's strength from the upper drifts and the lower rudder resisted torque by the strength of the longitudinal grain connected.

Glass will add some strength but will it be as much as the original design?

They look so simple at first but these rudder designs and their materials evolved over a long time and much use.

It will be great to hear what others with experience recommend Paul.